Problem: Solve for $x$ and $y$ using elimination. ${2x-y = 2}$ ${5x-4y = -4}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-4$ ${-8x+4y = -8}$ $5x-4y = -4$ Add the top and bottom equations together. $-3x = -12$ $\dfrac{-3x}{{-3}} = \dfrac{-12}{{-3}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {2x-y = 2}\thinspace$ to find $y$ ${2}{(4)}{ - y = 2}$ $8-y = 2$ $8{-8} - y = 2{-8}$ $-y = -6$ $\dfrac{-y}{{-1}} = \dfrac{-6}{{-1}}$ ${y = 6}$ You can also plug ${x = 4}$ into $\thinspace {5x-4y = -4}\thinspace$ and get the same answer for $y$ : ${5}{(4)}{ - 4y = -4}$ ${y = 6}$